If the half life for the radioactive decay of zirconium 84 is 26 minutes and i start with a 175 gram sample, how much will be left over after 104 minutes? show work or explain your answer.

10.94 g.

Explanation:

The decay of zirconium 84 is a first order reaction.The rate constant of the reaction (k) in a first order reaction = ln (2)/half-life = 0.693/(26.0 min) = 0.02665 min⁻¹.The integration law of a first order reaction is:

kt = ln [A₀]/[A]

k is the rate constant = 0.02665 min⁻¹.

t is the time = 104.0 min.

[A₀] is the initial percentage of radioisotope = 175.0 g.

[A] is the remaining percentage of radioisotope = ??? g.

∵ kt = ln [Ao]/[A]

∴ (0.02665 min⁻¹)(104.0 min) = ln (175.0 g)/[A]

2.772 = ln (175.0 g)/[A]

Taking exponential to both sides:

15.99 = (175.0 g)/[A]

∴ [A] = (175.0 g)/(15.99) = 10.94 g.

It shows that the experiment is designed properly.

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